If we will have to find the price for the sponge cake, or maybe we have to find out how much half as much flour is worth.

Then we moved on to next part of providing questions that would go with the calculations. This was so very tough for my kids. While 21 of 31 kids could come up with the correct question for part (a), they were lost with what to write for the other three parts.

Because we didn’t care what the numerical answers were, the kids didn’t do any calculations, instead they were supposed to focus on the operation(s) in each problem and decide on the question that would prompt a specific operation.

The most common question for part (b) was, “How much does 1 kg of flour cost?” (I’d swapped out £ for $.)

Then my next step would be for them to go ahead and use a calculator to get the numerical answers. They will see that for part (b), 24 divided by 21.50 equals approximately 1.12. And if 1.12 were the cost for 1 kg of flour, then 24 kg of flour should cost more than $24. But, wait. We already know that the bag of flour costs $21.50. Hopefully they’ll arrive at this contradiction on their own, and re-think their question.

We’ll then attach the units to the numbers accordingly and let the conversations continue. When kids tell me that they will calculate two numbers using operation w, I always follow up with, What does your answer mean? What unit or units does it carry?

Too often kids have trouble with word problems. Too often they don’t know what to do with two numbers let alone a bunch of numbers. They guess at division when one number is big and one is small. They add when they see two fractions. They multiply because that was how they solved the last word problem.

I will also do this with my 8th graders because I suspect they will have trouble too. And this is exactly the kind of trouble we need to get into. Now rather than later. This task gets them thinking about ratios — which is like the most important math thing in all of the math things.

Steward is exactly right about this task. And I’m thankful he shared.

It was used as a fine example of how reversing the question can often lead to a more challenging task.

6 Comments

Great example of how to open up the game or the conversation instead of closing it with one answer. You give your kids a chance to solve other problems by letting them “write” their own problems for the answers.

I do like this way of looking at stuff, and I really like that the kids wanted to have the same weight units for both items.
I found this in Eureka Math grade 3
———–
4 L 342 mL + 2 L 214 mL
3 kg 296 g + 5 kg 326 g
———–
and I wept !!!!!

Oh my God. If I saw that in any textbook, I’d cry too. The sad thing is somehow that question passed inspection. We are all entitled to stupid ideas, but when we have collaborators cheering us to our carry out our stupid ideas, that’s just criminal. Now I want to punch someone in the face. Thanks, Howard.

Great problem, Fawn! It illustrates the how important units are in solving any “real world” problem. It reminds me of using dimensional analysis to change a miles per hour (miles/hour) quantity into a feet per second (feet/sec) quantity by multiplying by 1 in the form of equivalent quantities of 1 hour/60 min, 1 min/60 sec, 5280 ft/1 mile. For some reason that I’ve never figured out, this procedure has the fancy name of “dimensional analysis”. I’d rather call it a creative use of the identity property of multiplication.

I love Don Steward’s blog, but I don’t think I can subscribe to it through email and therefore forget to check it out on a regular basis. Thanks for sharing this! I’m going to post it to my own blog http://www.watsonmath, which has one, maybe two followers.

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[…] Sometimes a Professional Learning workshop can make you think. Sometimes they can make you so sleepy that you question whether there was any caffeine in that triple shot latte latte you just finished. Sometimes they can make you question how you teach and excite you to try new things. Luckily for me, I went to Amie Albrecht’s sessions at the 2016 MASA Conference just over a week ago. I’ve been trying some great things that have streamed through her twitter feed (@nomad_penguin), which she shared with teachers in her workshop. I have recently blogged about how I’m using Mary Bourassa‘s (@WODBmath) Which One Doesn’t Belong problems (wodb.ca/). I have transformed four problems that will (hopefully) magnify the amount of thought my students will have to apply to answer them using Fawn Nguyen’s (@fawnpnguyen) Reversing the Question method (fawnnguyen.com/reversing-the-question/). […]

[…] Sometimes a Professional Learning workshop can make you think. Sometimes they can make you so sleepy that you question whether there was any caffeine in that triple shot latte latte you just finished. Sometimes they can make you question how you teach and excite you to try new things. Luckily for me, I went to Amie Albrecht’s sessions at the 2016 MASA Conference just over a week ago. I’ve been trying some great things that have streamed through her twitter feed (@nomad_penguin), which she shared with teachers in her workshop. I have recently blogged about how I’m using Mary Bourassa‘s (@WODBmath) Which One Doesn’t Belong problems (wodb.ca/). I have transformed four problems that will (hopefully) magnify the amount of thought my students will have to apply to answer them using Fawn Nguyen’s (@fawnpnguyen) Reversing the Question method (fawnnguyen.com/reversing-the-question/). […]

[…] Sometimes a Professional Learning workshop can make you think. Sometimes they can make you so sleepy that you question whether there was any caffeine in that triple shot latte latte you just finished. Sometimes they can make you question how you teach and excite you to try new things. Luckily for me, I went to Amie Albrecht’s sessions at the 2016 MASA Conference just over a week ago. I’ve been trying some great things that have streamed through her twitter feed (@nomad_penguin), which she shared with teachers in her workshop. I have recently blogged about how I’m using Mary Bourassa‘s (@WODBmath) Which One Doesn’t Belong problems (wodb.ca/). I have transformed four problems that will (hopefully) magnify the amount of thought my students will have to apply to answer them using Fawn Nguyen’s (@fawnpnguyen) Reversing the Question method (fawnnguyen.com/reversing-the-question/). […]